Spinodal-like scaling behavior after a temperature quench across the first-order phase transition in three-dimensional q -state Potts models

We study the out-of-equilibrium spinodal-like behavior of three-dimensional (3D) q -state Potts models (for q ⩾ 3 ), observed when the temperature is quenched across the first-order transition (FOT) point β fo = T fo − 1 . We consider a standard quench protocol, in which high-temperature configurations, thermalized at β i < β fo , are driven across the FOT by a purely relaxational dynamics at β > β fo . We focus on the emergence of spinodal-like behaviors in the thermodynamic limit, associated with the dynamic phase change. We argue that, if the nucleation of smooth droplets is the relevant mechanism of the post-quench phase change, for sufficiently small β fo − β i > 0 , the time-dependent energy density should scale in terms of ρ = ( ln ⁡ t ) 3 / 2 δ , where δ = β / β fo − 1 , with a discontinuity at a particular value ρ = ρ s > 0 . This implies the emergence of a spinodal-like behavior, whose time scale τ increases exponentially as ln ⁡ τ